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Widely employed for the accurate solution of the electroencephalographyforward problem, the symmetric formulation gives rise to a first kind,ill-conditioned operator ill-suited for complex modelling scenarios. This workpresents a novel preconditioning strategy based on an accurate spectralanalysis of the operators involved which, differently from otherCalder\'on-based approaches, does not necessitate the barycentric refinement ofthe primal mesh (i.e., no dual matrix is required). The discretization of thenew formulation gives rise to a well-conditioned, symmetric, positive-definitesystem matrix, which can be efficiently solved via fast iterative techniques.Numerical results for both canonical and realistic head models validate theeffectiveness of the proposed formulation.

A New Refinement-Free Preconditioner for the Symmetric Formulation in Electroencephalography